Councillor Geoffrey Theobald was re-elected as leader for the fifth year running and Councillor Dee Simson was re-elected as the other deputy leader.
Councillor Wealls replaces long-serving councillor and former Hove Borough Council leader Garry Peltzer Dunn.
The Conservatives gained two seats in the local elections on Thursday (7 May) but remain the largest opposition group on Brighton and Hove City Council, with 20 out of the 54 seats.
Labour is the biggest group, with 23 councillors, and is expected to form a minority administration. The Greens have 11 councillors.
Councillor Theobald said: “I am delighted that my colleagues have given me the honour of leading the Conservative group for another year and I would like to thank them for their support.
“I have an excellent and united team behind me and although we are disappointed not to be in administration, we are confident about what the future holds.
“I would also like to thank Councillor Garry Peltzer Dunn for being such a hard-working and supportive deputy leader for the last four years.”
Councillor Wealls said: “I am really excited to be given this opportunity to be deputy leader of the Conservative group by my colleagues and I would like to thank them for their support.
“We had some really talented and enthusiastic young people elected as councillors last week, together with highly experienced colleagues, and so the future looks very bright for the Conservatives in Brighton and Hove.”
Councillor Simson said: “It is great to be given another vote of confidence by my group colleagues and I am now looking forward to getting stuck into the hard work that lies ahead, holding this new Labour administration to account.”